Piravena must make a trip from $A$ to $B,$ then from $B$ to $C,$ then from $C$ to $A.$ Each of these three parts of the trip is made entirely by bus or entirely by airplane. The cities form a right-angled triangle as shown, with $C$ a distance of $3000\text{ km}$ from $A$ and with $B$ a distance of $3250\text{ km}$ from $A.$ To take a bus, it costs Piravena $\$0.15$ per kilometer. To take an airplane, it costs her a $\$100$ booking fee, plus $\$0.10$ per kilometer. [asy]
pair A, B, C;
C=(0,0);
B=(0,1250);
A=(3000,0);
draw(A--B--C--A);
label("A", A, SE);
label("B", B, NW);
label("C", C, SW);
label("3000 km", (A+C)/2, S);
label("3250 km", (A+B)/2, NE);
draw((0,125)--(125,125)--(125,0));
[/asy]  To begin her trip she flew from $A$ to $B.$ Determine the cost to fly from $A$ to $B.$
Answer: The cost to fly is $\$0.10$ per kilometer plus a $\$100$ booking fee. To fly $3250\text{ km}$ from $A$ to $B,$ the cost is $$3250\times 0.10 + 100=325+100=\boxed{\$425}.$$